distributedrangedifferencebasedtargetlocalizationinsensornetwork-外文文献(编辑修改稿)

distributedrangedifferencebasedtargetlocalizationinsensornetwork-外文文献(编辑修改稿)内容摘要：

esˆθ[n] = ˆθ[n−1] + K[n]parenleftbigb[n]− aT[n]ˆθ[n−1]parenrightbig (1)K[n] = Σ[n−1]a[n]1 + aT[n]Σ[n−1]a[n]Σ[n] = parenleftbigI − K[n]aT[n]parenrightbigΣ[n−1] (2)and index n corresponds to the nth sensor.IV. DATA MODELA static acoustic target generating a WSS Gaussian randomobservation process, s(t), is assumed where the intensity attenuates at the rate that is inversely proportional to the distancefrom the target. Perturbed by additive Gaussian measurementnoise wi(t), the received signal at ith sensor is given byxi(t) = s(t−τi)Di + wi(t). The energy can be calculated byaveraging over a time window T = Mfs where M is thenumber of samples and fs is the sampling frequency asyi[k] = 1M summationtextkMj=(k−1)M+1 x2i[j]. Assuming s(t) and w(t) areindependent, we getE{yi[k]} = E{s2(t)}D2i +E{w2(t)} (3)var{yi[k]} =2(E{s2(t)}D2i+E{w2(t)})2M (4)Let s(t) ∼ N(0,σ2s) and the noise at each sensor hasthe same distribution so that wi(t) ∼ N(0,σ2w). The signalPSD (Gs(f)), the noise PSD (Gw(f)), and the coherenceare assumed to be flat over a bandwidth ∆f Hz centeredat frequency f0. The SNR at each sensor, Gs,i(f)Gw,i(f) = σ2sD2iσ2w.According to [10], CRB of the TDE estimate is the followingσ2ij ≥braceleftbigg8Tpi23bracketleftbigg Cij1−Cijbracketrightbiggbracketleftbigg(f0 + ∆f2 )3 −(f0 − ∆f2 )3bracketrightbiggbracerightbigg−1where Cij = 1(1 + Gs,i(f)Gw,i(f)−1)(1 + Gs,j(f)Gw,j(f)−1)It is simple to derive that the variance of the estimate canbe in the form, σ2i1 = σ21 +αD2i , whereσ21 = 3D218Tpi2((f0 + ∆f2 )3 −(f0 − ∆f2 )3)SNR0α = 3(1 +D21SNR0)8Tpi2((f0 + ∆f2 )3 −(f0 − ∆f2 )3)SNR0 (5)and SNR0 denotes σ2sσ2w. Please note that σ2i1 is the varianceof TDE between ith sensor and the reference sensor asassumed in the previous section. Such variance is proportionalto D2i where the constants, σ21 and α are functions of D21.Therefore, with a fixed reference sensor, TDE with respect tothe farther sensors from the target is less accurate.V. DISTRIBUTED LOCALIZATIONFrom the description of the range difference based localization method, we can note that there are two key steps which areTDOA estimation and target localization obtained by solvingleast square equations. In a Centralized scheme, both stepstake place at the cluster head. The cluster head should bea reference sensor and TDOAs with respect to the clustermembers can be obtained through time delay estimation. Thedistributed localization concepts can be adopted by enablingsome processes to occur at each participating sensor, notjust at the cluster head. If time series data collected at thecluster head is transmitted to the participating sensors, timedelay estimation can be operated there. Broadcasting the datafrom one reference sensor to many participating sensors isexpected to require less total munication overhead thanin the opposite direction. Solving least square equations enpasses two mechanisms depending on whether batch orsequential procedure is applied. Batch estimator requires allmeasurements available at the same time whereas sequentialestimator needs only the estimate obtained from the (n−1)thsensor and a TDOA corresponding to the nth sensor. Thelatter, however, demands less putational plexity as itdoes not have to deal with matrix inversion which might beburdensome when the matrix is large due to a large numberof participating sensors. Another advantage is that the currentestimate can be used as the prior information to properly selectthe next participating sensor. According to the data model thatthe variance of time delay estimation is proportional to thesquare distance between the sensor and the target, the preferredsensors can be simply selected by considering the nearestsensors to the current estimate. Consequently, bining theideas of distributed processing for time delay estimation andsequential least square localization is expected to improve thelocalization performance in terms of both munication costsavings and accuracy. By using the notations defined in theprevious section, we propose the following algorithm:1) The sensor which receives the highest average signalenergy in a certain time window is selected to be aninitial sensor. Please note that the term “initial sensor”is used to call the sensor that starts the process insteadof “cluster head”.2) The initial sensor broadcasts collected time series datato at most k nearest neighbors within the maximumradio range where k is the initial expected number ofparticipating sensors. There might be a possibility thatless than k sensors can be reached depending on thecoverage of the radio range and the density of the sensorfield.3) Each neighbor operates time delay estimation using timeseries data collected at the sensor and the one sent fromthe initial sensor to estimate TDOAs.4) The initial estimate is obtained by using batch estimatorbased on TDOAs puted by the three nearest neighbors. The neighbor might be requested to broadcast timeseries data received from the initial sensor if there areless than three sensors that have already received it.5) k−4 nearest sensors to the initial estimate achieved fromthe batch estimator are expected to participate in thesequential least square method. It bees k−i nearestsensors for the following estimate where i is a numberof sensors that are already included in the localizationprocess.6) The route。